Let f(x) = root x. If the rate of change of f at x = c is twice its rate of change at x=1, then c=...?

i have no idea what to do.

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- Jan 7th 2007, 03:41 PMabcocoarate of change type
Let f(x) = root x. If the rate of change of f at x = c is twice its rate of change at x=1, then c=...?

i have no idea what to do. - Jan 7th 2007, 11:01 PMearboth
Hello,

the rate of change is calculated by the first derivative:

$\displaystyle f'(x)=\frac{df}{dx}=\frac{1}{2 \sqrt{x}}$

Now calculate f'(1) = 1/2. That means you know now the value of the rate of change at c: It is 1. Therefore solve the following equation for c:

$\displaystyle f'(c)=\frac{1}{2 \sqrt{c}}=1$. I've got $\displaystyle c=\frac{1}{4}$

EB